Information on Result #672970

Linear OA(2128, 2076, F2, 23) (dual of [2076, 1948, 24]-code), using construction X applied to Ce(22) ⊂ Ce(18) based on
  1. linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  2. linear OA(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(2128, 2076, F2, 22) (dual of [2076, 1948, 23]-code) [i]Strength Reduction
2Linear OA(2129, 2077, F2, 23) (dual of [2077, 1948, 24]-code) [i]Code Embedding in Larger Space
3Linear OA(2130, 2078, F2, 23) (dual of [2078, 1948, 24]-code) [i]
4Linear OA(2131, 2079, F2, 23) (dual of [2079, 1948, 24]-code) [i]
5Linear OA(2132, 2080, F2, 23) (dual of [2080, 1948, 24]-code) [i]
6Linear OA(2127, 2075, F2, 22) (dual of [2075, 1948, 23]-code) [i]Truncation
7Linear OOA(2128, 1038, F2, 2, 23) (dual of [(1038, 2), 1948, 24]-NRT-code) [i]OOA Folding
8Linear OOA(2128, 692, F2, 3, 23) (dual of [(692, 3), 1948, 24]-NRT-code) [i]
9Linear OOA(2128, 519, F2, 4, 23) (dual of [(519, 4), 1948, 24]-NRT-code) [i]
10Linear OOA(2128, 415, F2, 5, 23) (dual of [(415, 5), 1947, 24]-NRT-code) [i]
11Linear OOA(2128, 346, F2, 6, 23) (dual of [(346, 6), 1948, 24]-NRT-code) [i]
12Linear OOA(2128, 296, F2, 7, 23) (dual of [(296, 7), 1944, 24]-NRT-code) [i]
13Linear OOA(2128, 259, F2, 8, 23) (dual of [(259, 8), 1944, 24]-NRT-code) [i]